自动微分与生物学微分方程模型的优化
Automatic differentiation and the optimization of differential equation models in biology
AI总结：
本文阐述自动微分在优化微分方程模型轨迹中的应用，并指出该计算突破将推动生物学动态系统的理论与统计研究。
摘要：
一场计算革命释放了人工神经网络的威力。这场革命的核心是自动微分，它计算性能度量相对于大量参数的导数。微分增强了在大型模型中发现改进性能的能力，这是以前困难或不可能实现的成就。最近，第二项计算进展优化了微分方程所描绘的时间轨迹。优化需要对轨迹上的性能度量（例如跟踪环境的接近程度）相对于微分方程的参数进行微分。由于模型轨迹通常通过多步算法（如龙格-库塔法）进行数值计算，因此自动微分必须贯穿数值算法。本文解释了如何实现这种轨迹的自动微分。它还讨论了为什么这类计算突破可能推进生物学问题的理论和统计研究，在这些研究中，人们可以将变量视为时间和空间上的动态路径。在提高计算学习模型在性能景观上的成功率、提高进化适应度在适应景观上的成功率以及提高统计拟合在信息景观上的数据拟合度之间，出现了许多常见问题。
英文摘要：
A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters. Differentiation enhances the discovery of improved performance in large models, an achievement that was previously difficult or impossible. Recently, a second computational advance optimizes the temporal trajectories traced by differential equations. Optimization requires differentiating a measure of performance over a trajectory, such as the closeness of tracking the environment, with respect to the parameters of the differential equations. Because model trajectories are usually calculated numerically by multistep algorithms, such as Runge-Kutta, the automatic differentiation must be passed through the numerical algorithm. This article explains how such automatic differentiation of trajectories is achieved. It also discusses why such computational breakthroughs are likely to advance theoretical and statistical studies of biological problems, in which one can consider variables as dynamic paths over time and space. Many common problems arise between improving success in computational learning models over performance landscapes, improving evolutionary fitness over adaptive landscapes, and improving statistical fits to data over information landscapes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
